(a)
\(\mathrm {sdist}(x,\partial E_k) \rightarrow \mathrm {sdist}(x,\partial E)\)  locally uniformly in \(\mathbb {R}^2;\)
(b)
\(E_k\overset{K}{\rightarrow }\overline{E}\)  and \(\mathbb {R}^2\setminus E_k\overset{K}{\rightarrow }\mathbb {R}^2\setminus \mathrm {Int}(E),\) 
where \(K\) –Kuratowski convergence of sets [1]}.

